The effect of isoscalar S-wave multichannel $\pi \pi \to \pi \pi ,K\overline{K},\eta \eta$ scattering is considered in the analysis of decay data of the $\mathrm{\Upsilon }$-mesons. We show that when allowing for the final state interaction contribution to the decays $\mathrm{\Upsilon }(mS)\to \mathrm{\Upsilon }(nS)\pi \pi$ ($m>n,m=2,3,n=1,2$) in our model-independent approach, we can explain the two-pion energetic spectra of these $\mathrm{\Upsilon }$ transitions including the two-humped shape of the di-pion mass distribution in $\mathrm{\Upsilon }(3S)\to \mathrm{\Upsilon }(1S)\pi \pi$ as the coupled-channel effect. It is shown also that the considered bottomia decay data do not offer new insights into the nature of the $f_0$ mesons, which were not already deduced in our previous analyses of pseudoscalar meson scattering data.

• Received 23 December 2014

DOI:https://doi.org/10.1103/PhysRevD.91.037901